a 2.0 kg box is at rest on a table, The static friction coefficient μs between the box and table is 0.40, and the kinetic friction coefficient μk is 0.2
Then, a 25N horizontal force is applied to the box.
What is the best estimate of the magnitude of the box's acceleration?
Answers
The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².
How to determine the box's acceleration?In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.
Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:
F = μkN = μk(mg)
Where:
μk is the coefficient of kinetic frictional force.N is the normal force.m is the mass.g is the acceleration due to gravity.Substituting the given parameters into the formula, we have;
F = 0.20 × 2.0 × 9.81
F = 3.924 Newton.
By applying Newton's second law of motion, the net force is given by:
∑Fx = Applied force - kinetic frictional force = ma
Acceleration, a = [Applied force - kinetic frictional force]/m
Acceleration, a = [25 - 3.924]/2
Acceleration, a = 21.076/2
Acceleration, a = 10.538 ≈ 11 m/s²
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Related Questions
the time to failure of a television tube is estimated to be exponentially distributed with a rate of 3 per year. a company offers insurance on these tubes for the first year of usage. on what percentage of policies will they have to pay a claim?
Answers
On 4.98% of the policies, they will not have to pay a claim.
The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur. What are the chances of receiving a head, for instance, when we toss a coin in the air? The number of outcomes that could occur is the basis for the response to this question. The outcome in this case might be either head or tail. Therefore, there is a 50% chance that the result will be 1 / 2 head.
λ = 3 per year
To avoid having to pay a claim for these tubes, we need to determine the likelihood that they will live longer than a year.
Given by: The likelihood of tubes lasting longer than a year is
P(x > 1) = e^-λ*x
P(x > 1) = e³*¹ = 0.04978
Therefore, they won't be required to pay a claim on 4.98% of the policies.
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Experimental and theoretical see pic
Answers
1) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
2) Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
Explanation:N(Pennies) = 6
N(Nickels) = 8
N(Dimes) = 4
N(quarters) = 7
N(total) = 6 + 8 + 4 + 7
N(total) = 25
1) The theoretical probability of selecting a dime = 4/25
The experimental probability of selecting a dime = 30/150 = 1/5
B is wrong because theoretical probability is 4/25, not 9/50
Wrong statement:
The theoretical probability of selecting a dime is
Correct statement:
The theoretical probability of selecting a dime is 4/25
2) The experimental probability of selecting a penny = 45/200 = 9/40
The theoretical probability of selecting a penny = 6/25
Difference between experimental and theoretical probability = 6/25 - 9/40
Difference between experimental and theoretical probability = 3/200
Wrong statement:
The difference between the experimental and theoretical probability is 1/10
Correct statement:
The difference between the experimental and theoretical probability is 3/200
Use the order of operations to demonstrate that the Distributive Property holds by showing that both sides of each equation are equal.
RHS= 2*4/5*3+2*1/5*3
= /15+2/15
= +2/15
= /15
= /3
Answers
Applying the distributive property and precedence of operations, the results to each side of the expression is of 2/5, hence they property holds.
Left-hand side:The left-hand side of the expression is defined as follows:
2/5(4/3-1/3)
Applying the distributive property, 2/5 multiplies each term as follows:
2/5(4/3-1/3) = 8/15 - 2/15
(multiplication of fractions -> multiply numerators and denominators with themselves).
They have common denominator, then the subtraction of the fractions is calculated as follows:
2/5(4/3-1/3) = 8/15 - 2/15 = 6/15
6 and 15 are divisible by 3, hence the fraction is simplified as follows:
6/15 = 2/5.
Right-hand sideThe right-hand side of the expression is given as follows:
2/5 x 4/3 - 2/5 x 1/3
We have two operations, subtraction and multiplication. The multiplication has higher precedence, hence:
2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15
Then the procedure is the same as the left-hand side, obtaining an equal result, and so the distributive property holds.
Missing information2/5(4/3-1/3)=2/5*4/3-2/5*1/3
We need to solve:
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step by step explanation 6 divided by 396 show work
Answers
The value of 6 divided by 396 is 0.1515.
What is division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.
The steps include:
Step 1: Take the first digit of the dividend from the left.
Step 2: Divide it by the divisor and write the answer on top as the quotient.
Step 3: Subtract the result from the digit and then write the difference below.
Step 4: Bring down the next digit of the dividend.
In this case, 6/396 will give the value illustrated above.
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suppose an opaque jar contains 4 red marbles and 11 green marbles. this exercise refers to the experiment of picking two marbles from the jar without replacing the first one. what is the probability of getting a green marble first and a red marble second?
Answers
The probability of getting a green marble first and a red marble second exists 5/26.
What is meant by probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given: Red marbles = 3
Green marbles = 10
So, the total marbles = 3 + 10 = 13
Probability = Favorable outcomes / Total outcomes
Since, here replacement is not allowed,
Therefore, the probability of getting a green marble and a red marble
= first red and second green + first green second red
= 3/13 × 10/12+ 10/13 × 3/12
= 2 × 3/13 × 10/12
= 30/78
= 5/13
The probability of getting a green marble first and a red marble second
= 10/13 × 3/12
= 30/156
= 5/26
Therefore, the probability of getting a green marble first and a red marble second exists 5/26.
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The domain of the given function is ____ (use integers of fractions for any numbers in the expression.)f(z) = 5z²- 6z+2 —————- 6z² +5
Answers
Given:
[tex]f(z)=\frac{5z^2-6z+2}{6z^2+5}[/tex]Required:
To find the domain of the given function.
Explanation:
Now consider
[tex][/tex]Periodic Deposit: $? at the end of each monthRate: 7.5% compounded monthlyTime: 3 yearsFinancial Goal: $35,000O A. $2,628; $31,536 from deposits and $3,464 from interestB. $776; $27,936 from deposits and $7,064 from interestO c. $933; $33,588 from deposits and $1,412 from interestOD. $870; $31,320 from deposits and $3,680 from interest
Answers
Answer:
D. $870; $31,320 from deposits and $3,680 from interest
Explanation:
In order to calculate the monthly payment, we use the formula below:
[tex]P=\frac{A\mleft(\frac{r}{n}\mright)}{\mleft[\mleft(1+\frac{r}{n}\mright)^{nt}-1\mright]}[/tex]Given:
• The Financial Goal, A= $35,000
,• Rate = 7.5% = 0.075
,• Number of compounding period = 12 (Monthly)
,• Time, t = 3 years
Substitute into the given formula:
[tex]\begin{gathered} P=\frac{35000\mleft(\frac{0.075}{12}\mright)}{\mleft[\mleft(1+\frac{0.075}{12}\mright)^{12\times3}-1\mright]} \\ P\approx\$870 \end{gathered}[/tex]The monthly payment is $870.
[tex]\begin{gathered} \text{Total deposit}=870\times36=31,320 \\ \text{Interests}=35,000-31,320=3680 \end{gathered}[/tex]Option D is correct.
Which is the polynomial for the given graph?
a) P(x) = (x + 2)(x + 8)(x-1)(x-4)
b) P(x)=(x-2)(x + 1)²(x+4)
c) P(x) = (x-2)(x-8)(x + 1)(x+4)
d) P(x) = (x + 2)(x-1)²(x-4)
Answers
The polynomial for the given graph is P(x) = (x+2)(x+8)(x-1)(x-4)
Define polynomial.A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
Given,
The polynomial for the given graph is:
P(x) = (x+2)(x+8)(x-1)(x-4)
Each non-zero term in a polynomial function is made up of a number, known as the term's coefficient, and a variable raised to a non-negative integer power. A polynomial function can be either zero or the sum of a finite number of non-zero terms.
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Triangle STU, with vertices S(2,2), T(7,3), and U(5,6), is drawn inside a rectangle, as
shown below.
10
Answer: A =
A =
10
00
7
6
5
S
T
What is the area, in square units, of triangle STU?
10
units²
Submit Answer
Answers
The required area of triangle Δ STU would be 4 square units.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.
The given triangle Δ STU, with vertices S(2,2), T(7,3), and U(5,6), is drawn inside a rectangle.
The area of triangle Δ STU = rectangle ABCS - Δ ABS - Δ BTU - Δ STC
The area of triangle Δ STU = 4 × 5 - 1/2 × 3 × 4 - 1/2 × 5 × 1 - 1/2 × 3 × 2
The area of triangle Δ STU = 8/2
The area of triangle Δ STU = 4 square units
Hence, the required area of triangle Δ STU would be 4 square units.
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what is the slope of a line perpendicular to the line whose equation is 15x + 12y = -108
Answers
First, rewrite the equation in its slope intercept form:
(slope intercept form: y = mx + b where m = slope ; b = y-axis intercept)
15x + 12y = -108
Subtract 15x from both sides:
15x + 12y - 15x = -108 - 15x
12y = -108 - 15x
Divide both sides by 12:
12y/12 = (-108 - 15x)/12
y = -5x/4 - 9
As you can see the slope of this line is -5/4
Now, two lines are perpendicular if:
m1*m2 = -1
Where:
m1 = Slope of the line 1
m2 = Slope of the line 2
m1 in this case would be -5/4
so:
-5/4* m2 = -1
Solving for m2:
m2 = -1/(-5/4) = 4/5 = 0.8
Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $84 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answers
Step-by-step explanation:
Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $84 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? (Use m for the number of miles driven, and solve your inequality for m.)
inequality: 0.6m + 75 < 84
subtract 75 from both sides:
0.6m + 75 - 75 < 84 - 75
0.6m < 9
divide both sides by 0.6:
0.6m/0.6 < 9/0.6
m < 15
SO:
For anything less than 15 miles, Company A charges less than Company B.
solving one step inequalities using addition subtraction multiplication and division
Answers
To begin with
we have the inequality
[tex]4>x-2[/tex]To solve
Step 1: we will collect like terms
[tex]4+2>x[/tex]simplify the inequality above
[tex]\begin{gathered} 6>x \\ \text{Re}-\text{arranging} \\ x<6 \end{gathered}[/tex]Hence, the answer is
[tex]x<6[/tex]To draw the shape
Part B is correct
please fill in the missing
Answers
According to Table B, There is a series that is being followed next, i.e.,
m = (m+1) * (m-1)
In the given data,
Input is 5, then given output is 6 * 4, similarly
Input is 10, then given output is 11 * 9 which implies that
Output is the products of one more than input and one less than input
⇒5 = (5+1) * (5-1)
⇒5 = 6 * 4
again with 15 = (15+1) * (15-1) ⇒ 16 * 14
with 300 = (300+1) * (300-1) ⇒ 301 * 299
At last, we can construct a series from these data,
m = (m+1) * (m-1)
Where m is input and (m+1) * (m-1) is output of data.
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Kinsley opened a savings account and deposited 600.00 the account earns 5%interest compounded quarterly if she wants to use the money to buy a new bicycle in 3 years how much will she be able to spend on the bike
Answers
P : Principal amount deposited : $600
r : interest rate : 5 % = 0.05 ( decimal form)
n : number of compounding periods in a year : 4 (4 times in a year)
t : years
Apply compound interest formula:
A= P (1+r/n)^nt
Replace by the values given:
A = 600 (1+0.05/4)^(4.3)
A = 600 ( 1.0125) ^12
A =$ 696.45
each year, nordstrom sets up a gift-wrapping station to assist its customers with holiday shopping. preliminary observations of one worker at the station produced the following sample time (in minutes per package): 3.5, 3.2, 4.1, 3.6, 3.9. based on this small sample, what number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of ? [px]
Answers
Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy are 16.
Sample timings as observed are 3.5, 3.1, 4.0, 3.5, and 3.9.
Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5
The average sample time (X) is 3.6.
Observed time (T) Mean (X) (X - T) (X - T)^2
3.5 3.6 0.1 0.01
3.1 3.6 0.5 0.25
4.0 3.6 -0.4 0.16
3.5 3.6 0.1 0.01
3.9 3.6 -0.3 0.09
Allow Standard deviation to be S.
2 in (X-T) - 1 n
[tex]S=\sqrt{\frac{0.52}{4}}[/tex]
S = 0.3605
Considering that (h) = 0.05,
Given that 95% of the time,
Z value at 95% confidence interval = 1.96
Let N be the number of observations.
2 N= Z.S hX
[tex]N=(\frac{1.96X0.3605}{0.05X3.6})[/tex]
N = 15.4
N = 16 (rounded off to next whole number) (rounded off to next whole number)
Consequently, 16 observations are required.
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Answer:
Step-by-step explanation:
Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of 16.
Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5
The average sample time (X) is 3.6. Observed time (T) Mean (X) (XT) (X-T)^2
3.5 3.6 0.1 0.01
3.1 3.6 0.5 0.25
4.0 3.6 -0.4 0.16
3.5 3.6 0.1 0.01
3.9 3.6-0.3 0.09
Allow Standard deviation to be S.
2 in (X-T) - 1n
S=√0.52/4
S=0.3605
Considering that (h) = 0.05,
Given that 95% of the time,
Z value at 95% confidence interval = 1.96 Let N be the number of observations.
2 N=Z.S hx
N=(1.96X0.3605)÷(0.05×3.6)
N = 15.4
N = 16 (rounded off to next whole number) (rounded off to next whole number) Consequently, 16 observations are required.
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Is this a function (3,2) (-2,6) (3,3)
Answers
Answer:
No, it is not.
Step-by-step explanation:
A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.
A. On graph paper, draw a net that, when folded, will create this solid. B. Is there more than one possible net? Why or why not? C. Find the surface area and volume of this solid.
Answers
First of all, let's draw the net:
In which l= 3 units, h=2 units and w= 4 units.
The surface area will be:
SA= 2*h*w +2*l*w + 2*h*l
SA = 2*2*4 + 2*3*4 + 2*2*3
SA =16+24+12
SA= 52units²
The volume will be:
V=L*h*w
V= 3*2*4
V= 24 units³
(-7i)(3+3i)(a) Write the trigonometric forms of the complex numbers. (Let0 ≤ theta < 2pi.)(-7i) =(3+31) =(b) Perform the indicated operation using the trigonometric forms. (Let0 ≤ theta< 2pi.)(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
Answers
A complex number z is given in the form:
z = (x.y) = (realpart) x + imaginary part (iy)
In this case:
z1 = -7i
z2 = 3+3i
To write in trigonometric form:
[tex]\begin{gathered} z\text{ = r\lparen cos}\theta\text{ + isin}\theta) \\ For\text{ z1} \\ r\text{ = }\sqrt{0^2+7^2} \\ \text{ = 7} \\ \theta\text{ =}\tan^{-1}(\frac{7}{0} \\ Since\text{ t}he\text{ }argument\text{ }is\text{ }undefined\text{ }and\text{ y is negative,} \\ \theta=\text{ }\frac{3\pi}{2} \\ In\text{ trig form:} \\ z1\text{ = 7\lparen cos}\frac{3\pi}{2};sin\frac{3\pi}{2}) \\ For\text{ z2} \\ r\text{ = }\sqrt{3^2\text{ +3}^2} \\ \text{ =3}\sqrt{2} \\ \theta\text{ = }\tan^{-1}\frac{3}{3} \\ =\text{ }\frac{\pi}{4} \\ In\text{ trig form:} \\ z2\text{ = 3}\sqrt{2}(cos\frac{\pi}{4};sin\frac{\pi}{4}) \end{gathered}[/tex]Multiplication in trigonometric form:
[tex]z1*z2\text{ = \lparen21}\sqrt{2}\text{ \rparen \lparen cos}\frac{7\pi}{4};\text{ sin}\frac{7\pi}{4})[/tex]Multiplication in standard form:
[tex]\begin{gathered} (-7i)(3\text{ + 3i\rparen} \\ =-21i\text{ - 21i}^2 \\ i^2\text{ = -1} \\ =\text{ -21i + 21} \\ r\text{ = }\sqrt{21^2+21^2} \\ =21\sqrt{2} \end{gathered}[/tex]Find the distance between C & D. C = (8, -3) and D = (-9, -6) CD= [?] Round to the nearest tenth. Hint: Use the distance formula.
Answers
The distance between C and D is 17.26 units
What is meant by distance?
Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.
Distance CD = √{(-9-8)² + (-6+3)²}
= √{(-17)² + (-3)²}
= √{289 + 9}
= √298
= 17.26 units
Hence, the distance between C and D is 17.26 units
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Answer: 17.3
Step-by-step explanation:
What is 3 / 5 x 8/9?
A. 8 /15
B. 11 /14
C. 27 / 40
D. 91 /40
Answers
Answer:
A) 8/15
Step-by-step explanation:
3 / 5 x 8/9
(3/5)(8/9)
(3*8)/(5*9)
(24/45)
8/15
Answer:
8/15
Step-by-step explanation:
3 / 5 x 8/9
Multiplying fractions
Rewriting
3/9 * 8/5
Simplify
1/3 * 8/5
Multiply the numerators
1*8 =8
Multiply the denominators
3*5 = 15
8/15
Find the quotient of 0.744 by 6
Answers
[tex]0.744\div6[/tex]
Simplify:
[tex]\frac{0.744}{6}[/tex]
[tex]=0.124[/tex]
david drives from his home to the airport to catch a flight. he drives 3535miles in the first hour, but realizes that he will be 11hour late if he continues at this speed. he increases his speed by 1515miles per hour for the rest of the way to the airport and arrives 3030 minutes early. how many miles is the airport from his home?
Answers
David takes a car to get to the airport in time for his trip. 210 miles distance is the airport from his house in miles.
Given that,
David takes a car to get to the airport in time for his trip. He travels 35 miles in the first hour but understands that if he keeps going at this rate, he will be one hour late. For the final 15 miles to the airport, he speeds up by 15 mph and gets there 30 minutes early.
We have to find how far is the airport from his house in miles.
Distance traveled after 1 hour
Let us take the distance traveled after first 1 hour as y
Distance/speed = time
After 1 hour his speed = (35 + 15) = 50 mph
Total time count of 1 hour and 30 mins is 1.5 hr
y/50 + 1.5 = y/35
Multiply through by350
7y + 525 = 10y
3y = 525
y = 525/3
y = 175 miles
In the first 1 hour, at 35 mph, distance covered = 35 miles
Distance from his home to airport = 175 miles + 35 miles = 210 miles
Therefore, the distance between David's home and the airport is 210 miles.
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The cost of printing digital photos is given by c(p) = 0.15p, where p is the number of photos that you print and c(p) is the cost in dollars. Find c(75). c(75) = $
Answers
The value of the function c(75) for c(p) = 0.15p is c(75) = $11.25
How to determine the function value?From the question, the function definition is given as
c(p) = 0.15p
The above function is a linear function
This is so because it is represented as y = mx where m is the slope
The function value to calculate is given as
c(75)
This means that we calculate c(p) when p = 75
So, we have
c(75) = 0.15(75)
This gives
c(75) = 0.15 x (75)
Evaluate the product
c(75) = 11.25
Hence, the function value is c(75) = 11.25
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Please be quick!
Clare has been working to save money and wants to have an equation to model the amount of money in
her bank account.
She has been depositing $175 a month consistently. She doesn't remember how much money she
deposited initially; however, on her last statement she saw that her account has been open for 10 months
and currently has $2475 in it.
Write an equation for the amount of money in Clare's bank account after x months. Which equation form
did you choose?
Answers
The initial amount that was deposited by Clare is $725.
The equation for the amount of money in Clare's bank account after x months will be 725 + 175x
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let the amount deposited initially be x.
Based on the information, this will be illustrated as:
x + 175(10) = 2475
x + 1750 = 2475
Collect like terms
x = 2475 - 1750
x = 725
The initial amount is $725.
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Venus has a mean distance from the sun of 67,240,000 miles while mars has a mean distance from the sun of 4,213,000,000 miles. how much farther is mars from the sun than venus? a. 4,145,760,000 miles b. 4,146,260,000 miles c. 4,245,760,000 miles d. 4,280,240,000 miles
Answers
The Mean distance is 4,145,760,000 miles
The correct option is (a)
Given,
The mean distance from Venus to the sun is 67,240,000 miles.
The mean distance from Mars to the sun is 4,213,000,000 miles.
Now, According to the question
Subtract the distance of Mars to the sun from Venus to the sun :
Let's Calculate the mean distance:
= 4,213,000,000 - 67,240,000
= 4,145,760,000 miles
Hence, The Mean distance is 4,145,760,000 miles.
The correct option is (a)
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Simplify 8a^2 ➗ 4a
Asap please
Answers
Answer:
2a
Step-by-step explanation:
8a² / 4a
8/4 a²-¹
2a
please rate as brainliest
Answer:
2a
Step-by-step explanation:
8a^2 = 4a x 2a
8a^2 ➗ 4a
= ( 4a x 2a )/4a
= 2a
what expression can be used to add 1/2 plus 5/6?
Answers
Step-by-step explanation:
You can add the two fractions by turning 1/2 and 5/6 to have the same denominator. Turn 1/2 into a fraction with a denominator of 6. That simplifies to 1 1/3. Hope this helps yo
Given the frequency table, what percentage of the students that like rap are also in grades 9–10? Round to the nearest whole percent.
A. 16%
B. 38%
C. 40%
Answers
The percentage of students that like rap that are also in grades 9–10 = 32%.
What is a frequency table?A frequency table is the type of table that shows the number of occurrence of different types of variables of an experiment.
From the frequency table given;
In grade 9 - 10;
Rap students = 40 students
Rock students = 30 students
Country students = 55 students
The total students in grade 9 - 10 = 125
Therefore, the percentage of rap students in grade 9 - 10;
= 40/125×100/1
= 4000/125
= 32%
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Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
Answers
The person that has the higher average speed is Teresa.
How to find average speed?Average speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
Therefore, Karl drove 40 miles in 50 minutes and Teresa drove 35 miles in 42 minutes.
The person that has the higher average speed can be calculated as follows;
average speed of Karl = distance / time
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minutes
average speed of Teresa = distance / time
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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Kara is building a fence. The drawing above shows two sections of the fence. Help Kara figure out the
materials and cost for her project. Show all work. Use a calculator and round answers to the nearest
hundredth.
(a) The vertical fence posts are 5 feet tall. The diagonal pieces are 9 feet. How far apart should the fence posts be placed
(b) Kara's fence needs to reach at least 93 feet. How many fence posts will she need?
(c) How many diagonal pieces will she need?
(d) The fence posts cost $17 and the diagonal pieces cost $3.50. Calculate Kara’s total cost.
Answers
The materials and cost of Kara's project obtained using Pythagorean theorem, are;
(a) Distance between fence posts is 2•√(14) feet
(b) Kara needs about 12 fence posts
(c) Kara will need 22 diagonal pieces
(d) Kara's total cost is $281
What is the Pythagorean theorem?Pythagoras theorem can be stated as, the square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
The drawing obtained from a similar question consists of two diagonals between consecutive posts.
(a) The given parameters are;
Height of the fence post = 5 feet
Length of the diagonal pieces = 9 feet
The distance, d, between the fence posts using Pythagorean theorem gives;
d² = 9² - 5² = 56
d = 2•√(14)
The distances between the fence posts should therefore be 2•√(14) feet
(b) The number of fence posts, n, is given by the equation;
2•√(14) × n = 93
Which gives;
[tex] \displaystyle {n = \frac{93 }{2 \cdot \sqrt{14}} \approx 12.43}[/tex]
Given that after the 12th post, the 1st post comes next and the distance remaining is less than d, the number of posts, n is 12
(c) The number of diagonal pieces, m, needed, given that there are two diagonal pieces between two posts and there is only 11 in between spaces, gives;
m = 2 × 11 = 22
There are 22 diagonal pieces
(d) Cost of a fence post = $17
Cost of a diagonal piece = $3.5
Total cost, C, is therefore;
C = 12 × 17 + 22 × 3.5 = 281
Kara's total cost is $281
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