Answer:
Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have
$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.
Answer:
Let the width of the rectangle be w. Then the length of the rectangle is 5w.
The perimeter of a rectangle is the sum of all four sides. So, the perimeter of the rectangle is 2w+2(5w)=108 cm.
Simplifying the right side of the equation, we get 12w=108 cm.
Dividing both sides of the equation by 12, we get w=9 cm.
Since the width is 9 cm, the length of the rectangle is 5w=5(9)=45 cm.
Therefore, the length of the rectangle is 45 cm and the width is 9 cm.
(1/2 + 1/3) + [1/4 + (2/3)] ÷ 2/5 -4 x 5/6 ÷ 3/7
Answer:
Step-by-step explanation:
first, take 1/2+1/3 + 1/4+2/3
1/2+1/3=5/6 , 1/4+2/3=11/12
5/6+11/12=22/12
2/5-4=-18/5
-18/5*5/6=-3
22/12/3=22*3/12
=11/2
11/2/3/7=11/2*7/3
=77/6=12.8
Can you help me rewrite this in other words?
Part a
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
2. The chi square equals 1947 with one degree of freedom and the p-value being a non-zero number.
3. Since the p-value is less than the significance level, which would be .05, we rejected null hypothesis that would show that there is a significant association between climate change and a certainty.
Part 2
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
2. The chi square was 119.864 with 12 different degrees of freedom the p value for this is also a non-zero number.
3. Since the p value is less than .05, we would reject to null hypothesis, which would make sense that there is a significant association between sleeping and income class.
The discussion for both cases is shown below.
Part a:
H0: there is no association between climate change and certainty.
H1: there is no association between climate change and certainty.
It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.
The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.
Part 2:
H0: there is no association between sleeping and the income class.
H1: there is a association between the income class and sleeping.
Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.
Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.
In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.
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Jamar is going to invest $2200 and leave it in an account for 14 years. Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200
Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.
How is the interest rate for continuous compounding determined?Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:
Total P+I (A) = $4,200.00
Principal (P) = $2,200.00
Compound (n) = Compounding Continuously
Time (t in years) = 14 years
R = 4.619% per year
The calculation steps are as follows:
Solving for rate r as a decimal
r = ln(A/P) / t
r = ln(4,200.00/2,200.00) / 14
r = 0.0461877
Then convert r to R as a percentage:
R = r * 100
R = 0.0461877 * 100
R = 4.62%/year
Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.
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On January 10, 2022, Cullumber Co. sold merchandise on account to Robertsen Co. for $16,600, n/30. On February 9, Robertsen Co. gave Cullumber Co. a 11% promissory note in settlement of this account.
The preparation of the journal entry to record the sale and the settlement of the account receivable is as follows:
Journal Entry:January 10, 2022:
Debit Accounts Receivable $16,600
Credit Sales Revenue $16,600
(To record the sale of merchandise on account to Robertsen Co, n/30.)
February 9, 2022:
Debit Notes Receivable $16,600
Credit Accounts Receivable $16,600
(To record the receipt of a 11% promissory note in settlement of account receivable.)
What are journal entries?Journal entries refer to the initial records maintained about business transactions.
Journal entries show how the transactions will be posted in the general ledger.
Transaction Analysis:January 10, 2022: Accounts Receivable $16,600 Sales Revenue $16,600
Terms n/30
February 9, 2022: Notes Receivable $16,600 Accounts Receivable $16,600
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Question Completion:Prepare the journal entry to record the sale and the settlement of the account receivable.
Shane has 2 white shirts, 2 blue ones and 1 red one, He has gray pants and black pants. He hung them all up on hangers in his closet, but one shirt and a pair of pants fell on the floor. The probability that a red shirt and black slacks are on the floor is
Answer:
0.1
Step-by-step explanation:
P(red shirt, black pants | 1 shirt, 1 pants)
= P(red shirt | 1 shirt) * P(black pants | 1 pants)
= (1)/(2+2+1) * (1)/(2)
= 1/10
=0.1
A sidewall of a building is shown below. Apply a formula to find the area of the wall.
Answer:1020 ft (squared)
Step-by-step explanation:
Base width 1 (28 ft) x Base width 2 (40 ft) x height (6 ft) = 1020 ft (squared)
john want to buy a new bike that costs 337and he already has save 103 estimates to find about how much more john needs to save to buy the bike
To find the estimated amount John needs to save to buy the bike, we can subtract the amount he already has saved from the cost of the bike:
Estimated amount = Cost of bike - Amount already saved
Estimated amount = $337 - $103
Estimated amount = $234
Therefore, John needs to save an estimated $234 more to buy the bike.
Answer:
John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
Step-by-step explanation:
To find out how much more John needs to save to buy the bike, we can subtract the amount he has already saved from the cost of the bike:
337 - 103 = 234
Therefore, John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
Helpppppp pleaseeeee
The resulting matrix from an elementary row operation to get a 1, in row 1 column 1 is:
R₁ = [1 4 -8] and R₂ = [2 4 7]
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
The row operation R₁ - 4 — R₁ will be carried out as follows:
5 - 4 = 1 {row 1 column 1}
9 - 4 = 5 {row column 2}
-4 - 4 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 4 -8] and R₂ = [2 4 7]
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HELP its a matric or matrix problem I NEED IT SOLVED AS QUICK AS POSSIBLE PLEASE
Using the given matrix, the value of -10(T) is
[tex]-10(T) = \left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]
Multiplication of matricesFrom the question, we are to carry out the matrix multiplication
From the given information,
The given matrices is:
[tex]T =\left[\begin{array}{cc}23&-38\\17&-6\end{array}\right][/tex]
Now, we are to determine -10(T)
To achieve this, we will multiply each of the element in the given matrix by -10
That is,
-10 ×23 = -230
-10 × -38 = 380
-10 × 17 = -170
-10 × -6 = 60
Thus,
The result of the multiplication will be:
[tex]\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]
Hence, the value of -10(T) is
[tex]-10(T) = \left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]
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In urgent need of assistance pls and thanks
The addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5) and it has been represented by using the head to tail method in the graph below.
What is a vector?In Mathematics and Science, a vector can be defined as an element of a vector space, which represents an object that is composed of both magnitude and direction.
How to add vectors by using the head to tail method?In Mathematics and Science, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Generally speaking, the head to tail method of adding two (2) vectors involve drawing the first vector ([tex]\vec a[/tex]) on a cartesian coordinate and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Lastly, the resultant vector is then drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By solving the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)
[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))
[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]
[tex]\vec a + \vec b[/tex] = (3, -5).
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Jaswat set out to walk a distance of 12 Km. After walking for 1 1/2 hours at a speed of
6 Km/h, he had to slow down to steady pace of 4 Km/h , which he maintained till the
end of the journey. How long did he take to complete the journey?
Answer: 2 hours 15 minutes
Step-by-step explanation:
To solve this problem, we need to use the formula:
distance = speed x time
First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:
distance = speed x time
distance = 6 Km/h x 1.5 h
distance = 9 Km
So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.
Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:
distance = speed x time
3 Km = 4 Km/h x time
time = 3 Km / 4 Km/h
time = 0.75 hours = 45 minutes
Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.
Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign
A coach left woodlands and travelled towards Muar at an average speed of 50 Km/h.
Half an hour later, a car left Woodlands, travelled along the same route, and reached
Muar at 12.30 p.m. The distance between the two places was 150 km. The coach reached
Muar at 1.00 p.m
a) At what time did the car leave Woodlands?
b) What was the average speed of the car?
Answer:
a) 10:30 a.m.
b) 75 km/h
Step-by-step explanation:
You want to know the leaving time and speed of a car from Woodlands to Muar if it left half an hour later and arrived half an hour earlier than a coach that traveled the 150 km distance at a speed of 50 km/h and arrived at 1 p.m..
Travel timeThe travel time of the coach is found from the relation ...
time = distance/speed
time = (150 km)/(50 km/h) = (150/50) h = 3 h
Then the coach left Woodlands at ...
1 pm -3 h = 10 am
a) Leaving timeThe car left half an hour later than the coach, so left at 10:30 a.m..
b) SpeedThe car arrived at Muar at 12:30 p.m. so had a travel time of ...
12:30 -10:30 = 2 h
The speed over the 150 km distance is given by ...
speed = distance/time
speed = (150 km)/(2 h) = (150/2) km/h = 75 km/h
The average speed of the car was 75 km/h.
__
Additional comment
The car passed the coach at 11:30 a.m., when both had covered half the distance.
Solve for x. Round to the nearest tenth, if necessary.
x=15.4 units
Step-by-step explanation:First, some definitions before working the problem:
The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.
The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.
Working the problem
For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse. We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.
For this triangle, the "opposite" leg is known. Additionally, the "hypotenuse" is unknown and is our "goal to find" side.
Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".
Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh". So, the desired function to use for this triangle is the Sine function.
[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]
[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]
Multiply both sides by x, and divide both sides by sin(17°)...
[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]
Make sure your calculator is set to degree mode, and calculate:
[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]
[tex]x=15.391366289249...[/tex] units
Rounded to the nearest tenth...
[tex]x=15.4[/tex] units
Complete the worksheet below please
Answer:
x= 3 cm
Explanation:
I am bad at it
What is the relation between the variables in the equation
The equation x⁴/y = 7 represents a relationship of direct proportionality between x and y, where x⁴ and y are inversely proportional to each other.
The equation x⁴/y = 7 represents a relationship between the variables x and y. Specifically, it shows that the fourth power of x divided by y is equal to 7.
This equation can be rewritten as x⁴ = 7y, which means that if we know the value of y, we can determine the corresponding value of x that satisfies the equation. For example, if y = 1, then x⁴ = 7, and taking the fourth root of both sides of the equation gives us x = ± √7.
Conversely, if we know the value of x, we can solve for y by rearranging the equation as y = x⁴/7. This shows that y is directly proportional to x raised to the fourth power, meaning that as x increases, y will also increase, but at a faster rate due to the exponent of 4.
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Would like some help with this question, please.
Answer:
i believe 67 its somewhat hard to tell but the line seems to be in the middle between 150 and 140
Step-by-step explanation:
since it heats up to 212 then the person lets it cool down for 10 mins the temp goes to 145 (Answer is 67)
40
Selena is training for a race. Last week, she ran 4 miles each day on 3 different
days. Use the symbol X to make an array that represents the total number of miles
Selena ran last week.
Show your work.
The array that represents the total number of miles is X = 12
Given that;
Selena ran 4 miles per day
And she ran for 3 different days
Let the total miles she ran = X
therefore
X = miles of 1st day + miles of 2nd day + miles of 3rd day
⇒ X = 4 + 4 + 4
⇒ X = 12 miles
Thus the symbolic form of miles Selena ran is,
X = 12.
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The cost of 8 T-shirts and 3 jackets is $135. The cost of 7 T-shirts and 5 jackets is $149.
Enter the cost of one T-shirt and one jacket in the response boxes below.
T-shirt: S
jacket: $
The cost of one T-shirt and one jacket is $12 and $13 respectively.
What is the cost of one T-shirt and one jacket?Let
cost of one t-shirt = x
cost of one jacket = y
8x + 3y = 135
7x + 5y = 149
Multiply (1) by 5 and (2) by 3
40x + 15y = 675
21x + 15y = 447
Subtract the equations to eliminate y
40x - 21x = 675 - 447
19x = 228
divide both sides by 19
x = 228/19
x = 12
Substitute x = 12 into (1)
8x + 3y = 135
8(12) + 3y = 135
96 + 3y = 135
3y = 135 - 96
3y = 39
y = 39/3
y = 13
Hence, a T-shirt and a Jacket cost $12 and $13 respectively.
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Find the shortest path from vertex A to vertex L. Give your answer as a sequence of vertexes, like ABCFIL
The shortest path from vertex A to vertex L is ACFIL. The total distance of the path is 27 units.
To find the shortest path from vertex A to vertex L, we can use Dijkstra's algorithm. We start by marking the distance of each vertex from A as infinite except for A, which is 0. Then, we choose the vertex with the smallest marked distance and update the distances of its neighbors. We repeat this process until we reach L.
In this case, we would start at A and update the distances of B and D to 2 and 19, respectively. We would then choose B and update the distances of C, F, and E to 11, 10, and 18, respectively.
Next, we would choose F and update the distances of I and L to 27 and 30, respectively. Finally, we would choose L and have found the shortest path from A to L: ACFIL with a total distance of 27.
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assume that a sample is used to estimate a population proportion p. Find the margin of errorS that corresponds to the following: a 98% confidence ; the sample size is 800, of which 40% are successes
Answer:
Step-by-step explanation:
To find the margin of error for a 98% confidence level, we need to use the z-score that corresponds to this confidence level, which is 2.33 (found in a z-table or using a calculator).
The formula for the margin of error (E) is:
E = z*(sqrt(p*q/n))
Where:
z is the z-score for the desired confidence level (2.33 for 98% confidence)
p is the sample proportion (0.4, or 40%)
q is the complement of the sample proportion (1 - 0.4 = 0.6)
n is the sample size (800)
Substituting these values into the formula, we get:
E = 2.33*(sqrt(0.4*0.6/800)) = 0.045
So the margin of error for a 98% confidence level, with a sample size of 800 and a sample proportion of 40%, is 0.045 or approximately 4.5%. This means that we can be 98% confident that the true population proportion is within 4.5% of the sample proportion.
7 (a) A On the Venn Diagram, shade the region A N B
For A∩B , shade the middle common part in the Venn diagram.
What is Venn diagram?
Using circles to represent relationships between objects or limited groupings of objects, a Venn diagram is one example. Circles that overlap share certain characteristics, whereas circles that do not overlap do not. Venn diagrams are useful for showing how two concepts are related and different visually.
Here the given Venn diagram contains two sets A and B.
The A intersection B or A∩B means , common elements in both A and B.
So we have shade the middle part of Venn Diagram.
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Oscar buys his lunch in the school cafeteria the cost of 15 school lunches is 33.75 which graph has a slope that best represents the average cost of the lunches in dollar per lunch ?
Answer:
The graph should be increasing 2.25 each time
Step-by-step explanation:
Since Oscar buys his lunch in school cafeteria and the cost of 15 school lunches is 33.75
Divide them: 33.75 ÷ 15 =
and will represents the average cost of the lunches in dollar per lunch that is 2.25
solve for x in the diagram
Answer:
15.04 (3.s.f)
Step-by-step explanation:
Cos a = adjacent/ hypotenuse
Cos 43 = 11/ x
so,
x= 11 / cos 43
= 15.04
Find the approximate radius of a circle with a circumference of 23.21 feet. Use 3.14 for π
. Round to the nearest hundredth if necessary.
Thee radius of the circle is 3. 696 feet
How to determine the radiusThe formula that is used for calculating or determining the circumference of a circle is expressed as;
C = 2πr
Given that the parameters for the formula are expressed thus;
C is the circumferenceπ takes the constant value of 3.14r is the radius of the circleFrom the information given, we have that;
Radius = 23.21 feet
Substitute the values, we get;
23.21 = 2× 3.14r
Multiply the values
r = 23.21/6.28
Divide the values
r = 3. 696 feet
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La distancia entre Bay Town y Oak Glen es de 175 millas. Si la ecuación y = -x +175 representa la distancia que queda por recorrer hasta Oak Glen, ¿qué representa el dominio? ¿Qué es el dominio?
The correct answer is: D) distance traveled since leaving Bay Town; x ≥ 0
How to solveThe equation y = -x + 175 represents the distance left to travel to Oak Glen.
In this equation, x is the distance traveled since leaving Bay Town, and y is the distance left to reach Oak Glen.
The domain represents the possible values of x, which is the distance traveled since leaving Bay Town.
Since distance traveled cannot be negative, the domain is x ≥ 0. Therefore, the correct answer is:
D) distance traveled since leaving Bay Town; x ≥ 0
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The question in English is:
The distance between Bay Town and Oak Glen is 175 miles. If the equation y = -x +175 represents the distance to go to Oak Glen, what does the domain represent? What is the domain?
Consider the following triangle. A right triangle. The hypotenuse is 5 feet, the side opposite to angle theta is 3 feet, the side adjacent to angle theta is 4 feet. If sin Theta = three-fifths, what is the measure of the angle? a. 53.1º b. 36.9º c. 30.1º d. 59º
The measure of the angle is 36.9^o. Option B.
What is a right triangle?A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.
From the details given in the question, we can deduced that;
Sin θ = 3/5
= 0.6
So that,
θ = Sin^-1 0.6
= 36.87
θ = 36.9^o
The measure of the angle is 36.9^o. Option B.
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1. It is impossible to manufacture any product by mass production methods without some
items being defective. Most production facilities employ quality control specialists to
study the proportion of a product being manufactured that is defective. Suppose a quality control engineer needs to keep defective items at 5% (or less). The engineer collects a
sample of 50 items manufactured and calculates the sample proportion (^ )of defective
items. (P)
a. What is the population proportion of items manufactured that are defective?
The population proportion of items manufactured that are defective is estimated to be between 0.137 and 0.037 with a 95% confidence level.
What is Sample Proportion :The sample proportion, denoted as ^p, is the proportion of a certain characteristic or outcome in a sample. It is calculated by dividing the number of individuals in the sample that exhibit the characteristic or outcome of interest by the total number of individuals in the sample.
It is an estimate of the population proportion, denoted as p, which represents the proportion of the same characteristic or outcome in the entire population.
Here we have
The sample proportion (^) of defective items is not provided in the question.
Hence, let's assume that the sample proportion (^) of defective items is 0.05 (i.e., 5% as specified in the question).
The sample size is 50, and the sample proportion (^) is 0.05.
The question is asking for the population proportion of items manufactured that are defective (P).
Use the sample proportion (^) and the sample size to calculate the margin of error and construct a confidence interval.
Assuming a 95% confidence level, we can use the following formula to calculate the margin of error:
Margin of error = 1.96 × √(^×(1⁻^)/n)
Substituting the values, we get:
Margin of error = 1.96 × √(0.05 × (1 - 0.05)/50) = 0.087
To construct the confidence interval, we add and subtract the margin of error from the sample proportion:
Confidence interval = ^ ± margin of error
Confidence interval = 0.05 ± 0.087
Confidence interval = (0.137, 0.037)
Therefore,
The population proportion of items manufactured that are defective is estimated to be between 0.137 and 0.037 with a 95% confidence level.
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Assume that the speed of automobiles on an expressway during rush hour is normally distributed with mean of 62 mph and a standard deviation of 5 mph.
What percent of cars are traveling slower than 55 mph?
About 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
To solve this problemUsing the provided mean and standard deviation, we must standardize the value of 55 mph before determining the equivalent area under the standard normal distribution curve.
The standardized value, or z-score, is calculated as:
z = (x - μ) / σ
Where
x is the value we want to standardize (in this case, 55 mph) μ is the mean (62 mph)σ is the standard deviation (5 mph)Plugging in the values, we get:
z = (55 - 62) / 5 = -1.4
The area under the usual normal distribution curve to the left of z = -1.4 must now be determined. Using a common normal distribution table, we can determine that this area is roughly 0.0808.
Therefore, about 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.
Learn more about normal distribution here : brainly.com/question/27275125
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